Explicit non-Gorenstein R=T via rank bounds I: Deformation theory
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929711092858880 |
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| author | Hsu, Catherine Wake, Preston Wang-Erickson, Carl |
| author_facet | Hsu, Catherine Wake, Preston Wang-Erickson, Carl |
| contents | Ribet has proven remarkable results about non-optimal levels of residually reducible Galois representations. We focus on a non-optimal level $N$ that is the product of two distinct primes and where the Galois deformation ring is not expected to be Gorenstein. We prove a Galois-theoretic criterion for the deformation ring to be as small as possible -- that is, for there to be a unique newform of level $N$ with reducible residual representation. When this criterion is satisfied, we deduce an $R=\mathbb{T}$ theorem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2209_00536 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Explicit non-Gorenstein R=T via rank bounds I: Deformation theory Hsu, Catherine Wake, Preston Wang-Erickson, Carl Number Theory 11F80, 11F33 Ribet has proven remarkable results about non-optimal levels of residually reducible Galois representations. We focus on a non-optimal level $N$ that is the product of two distinct primes and where the Galois deformation ring is not expected to be Gorenstein. We prove a Galois-theoretic criterion for the deformation ring to be as small as possible -- that is, for there to be a unique newform of level $N$ with reducible residual representation. When this criterion is satisfied, we deduce an $R=\mathbb{T}$ theorem. |
| title | Explicit non-Gorenstein R=T via rank bounds I: Deformation theory |
| topic | Number Theory 11F80, 11F33 |
| url | https://arxiv.org/abs/2209.00536 |